bool lessThan(fraction x, fraction y) // non-member function returning a bool
{ // indicating if x < y
int xDen = x.getDenom();
int yDen = y.getDenom();
int lcm = LCM(xDen, yDen); // same code as add, mostly
int factor1 = lcm / xDen;
int factor2 = lcm / yDen;
return ((x.getNumer() * factor1) < (y.getNumer() * factor2));
}
fraction add(fraction x, fraction y) // non-member function to return a new
{ // fraction containing the sum of two others
int xDen = x.getDenom();
int yDen = y.getDenom();
int lcm = LCM(xDen, yDen); // it would be trivial to implement
int factor1 = lcm / xDen; // reduceMe here if desired.
int factor2 = lcm / yDen;
int num = (x.getNumer() * factor1) + (y.getNumer() * factor2);
fraction z = fraction(num, lcm);
return z;
}
bool operator<(const fraction &a, const fraction &b) {
double ax, ay;
int as;
getFrSpec(a.getNumer(), a.getDenom(), &ax, &ay, &as);
if(as == -1) { ax =- ax; ay =-ay; }
double bx, by;
int bs;
getFrSpec(b.getNumer(), b.getDenom(), &bx, &by, &bs);
if(bs == -1) { bx =- bx; by =-by; }
return (ax < bx || (ax == bx && ay < by));
}
const fraction operator*(const fraction &a, int64_t b) {
if(b < a.getInterimMultOverflowPt()) {
// b < interimMultOverflowPt
return fraction(b * a.getNumer(), a.getDenom());
} else if(b <= a.getFinalMultOverflowPt()) {
// interimMultOverflowPt <= b <= finalMultInterimPt
cerr << "fraction::operator*- an interim overflow has occurred\n";
return fraction(I64_MAX);
} else { // finalMultInterimPt < b
cerr << "fraction::operator*- a final overflow has occurred\n";
return fraction(I64_MAX);
}
}